Final answer:
To find the inverse of a function f(t), solve f(t)=y for t, and then reflect the relationship over y=x to get t=g(y), ensuring the original function is one-to-one.
Step-by-step explanation:
To find the inverse of a function, we essentially reverse the process of the function. If the original function is f(t), we want to find a function, often denoted as f-1(t), such that when it is applied to f(t), it returns the original input t. This means that for the function f(t), we solve the equation f(t)=y for t in terms of y. To get the inverse, we then reflect this relationship over the line y=x so that the new function has the form t=g(y). However, it's important to check that the function is one-to-one and therefore has an inverse that is also a function. Functions that are not one-to-one do not have an inverse that is a function because they fail the horizontal line test.